RANDOM PLASMA:
A plasma consists of a mixture of ions of mass Mi and free electrons of mass Me.
A random plasma consists of a volume of neutral plasma surrounded by a thin sheath with a positive space charge. Within the neutral plasma region at steady state each particle has approximately the same kinetic energy. Hence, within the neutral plasma:(Me / 2) Ve^2 = (Mi / 2) Vi^2
where:Ve = electron velocity;
andVi = ion velocity.

Within the neutral plasma there are equal numbers of ions and free electrons.

The positive space charge in the sheath surrounding the neutral plasma is balanced by a negative charge (a layer of surface electrons) at the enclosure wall. Within the positive space charge sheath the number of free electrons is very small and the positive ions are constantly drifting radially toward the enclosure wall. When they reach the wall they are neutralized and bounce back into the neutral plasma. The thickness of the space charge sheath is set by the electron radial kinetic energy component in the neutral plasma. When a plasma electron reaches the enclosure wall all of its initial kinetic energy component normal to the wall has converted to electric potential energy. Hence the electron has no momentum to impart to the enclosure wall.

However, an ion impacting the enclosure wall has both the kinetic energy that it had while in the neutral plasma plus the additional radial kinetic energy that it acquired crossing the charge sheath. Hence the momentum that the ion imparts to the wall is larger than for a neutral gas. Hence the force and pressure on the enclosure wall are larger than for a neutral gas. With these issues in mind we can follow the same pattern as for a neutral gas to derive the formula for the increase in particle kinetic energy resulting from adiabatic compression of a random plasma.

A distinguishing issue is that when a positive ion impacts the enclosing wall its kinetic energy component
normal to the wall is twice what it would be if the plasma was a gas at the same temperature. This increase
in impact kinetic energy significantly increases the liquid lead wall velocity required for adiabatic
compression of a random plasma, as is necessary in both the General Fusion MTF process and the Micro Fusion
International PIF process.

PLASMA HEAT LOSS AND GAIN:
Consider a random plasma in an enclosure with a stationary wall. Due to the positive sheath space charge surrounding the plasma the plasma electrons that reach the wall have almost no momentum normal to the wall. Hence most of the heat loss from the plasma is via plasma ion impacts with the wall.

The energy transfer per ion impact can be minimized by making the plasma ion very light, as are hydrogen isotopes, and by making the wall atoms very heavy, as is lead.

The heat loss from the plasma can be further reduced by rapidly moving the wall inwards towards the plasma so that there is no transfer of energy from the plasma to the wall. In the absence of such energy transfer there is almost no problem with the wall material sputtering into the plasma.

If the wall is moved fast enough towards the plasma there is adiabatic compression, that causes an increase in the per particle kinetic energy (temperature) in the plasma. The MTF and PIF processes both rely on increasing the per particle kinetic energy via adiabatic compression.

Energy exchange and hence heat loss via plasma ion to wall electron collisions is relatively small due to
the high mass ratio between the plasma ions and the wall electrons.